Write in Slope-Intercept Form 1/3x+2y=4/3

$\frac{1}{3} x + 2 y = \frac{4}{3}$

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Rewrite in slope-intercept form.

Simplify the left side.

Combine $\frac{1}{3}$ and $x$ .

$\frac{x}{3} + 2 y = \frac{4}{3}$

Subtract $\frac{x}{3}$ from both sides of the equation.

$2 y = \frac{4}{3} - \frac{x}{3}$

Divide each term in $2 y = \frac{4}{3} - \frac{x}{3}$ by $2$ and simplify.

Divide each term in $2 y = \frac{4}{3} - \frac{x}{3}$ by $2$ .

$\frac{2 y}{2} = \frac{\frac{4}{3}}{2} + \frac{- \frac{x}{3}}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{\frac{4}{3}}{2} + \frac{- \frac{x}{3}}{2}$

Divide $y$ by $1$ .

$y = \frac{\frac{4}{3}}{2} + \frac{- \frac{x}{3}}{2}$

Simplify the right side.

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{4}{3} \cdot \frac{1}{2} + \frac{- \frac{x}{3}}{2}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$y = \frac{2 (2)}{3} \cdot \frac{1}{2} + \frac{- \frac{x}{3}}{2}$

Cancel the common factor.

$y = \frac{2 \cdot 2}{3} \cdot \frac{1}{2} + \frac{- \frac{x}{3}}{2}$

Rewrite the expression.

$y = \frac{2}{3} + \frac{- \frac{x}{3}}{2}$

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{2}{3} - \frac{x}{3} \cdot \frac{1}{2}$

Multiply $- \frac{x}{3} \cdot \frac{1}{2}$ .

Multiply $\frac{1}{2}$ by $\frac{x}{3}$ .

$y = \frac{2}{3} - \frac{x}{2 \cdot 3}$

Multiply $2$ by $3$ .

$y = \frac{2}{3} - \frac{x}{6}$

Write in $y = m x + b$ form.

Reorder $\frac{2}{3}$ and $- \frac{x}{6}$ .

$y = - \frac{x}{6} + \frac{2}{3}$

Reorder terms.

$y = - (\frac{1}{6} x) + \frac{2}{3}$

Remove parentheses.

$y = - \frac{1}{6} x + \frac{2}{3}$